Look into replacing the coolant temp. sensor that sends signals to the
ECU.  MIGHT not be the problem, but it's $12 including the new o-ring
and easy to DIY.

Another probably cause would be O2 sensor, especially since shutting
off, even when hot, and restarting gives you a 2 minute reprieve.  The
ecu doesn't begin accepting signals from the O2 sensor until it is up to
temp.  It could cool off quick enough when you shut it off that it takes
2 minutes for the ecu to start accepting its signals again.

Tonya
87 Vanagon GL Wolfs
74 S. Beetle
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